Geometric properties and invariant manifolds of the Riccati equation

This short paper considers the general Riccati matrix differential equation. It reviews and extends results on the characterization and existence of equilibrium solutions, establishes that the Riccati equation has at most one stable equilibrium solution ast → → -∞, and confines the region of attraction to this unique stable equilibrium solution by identifying and utilizing linear and nonlinear invariant manifolds of the Riccati equation.